## Ocean Waves: The Stochastic ApproachWaves observed in the ocean are extremely irregular and, from a physics standpoint, it seems impossible to describe this chaotic situation. Scientists can describe the situation by means of a stochastic approach. This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves--information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins with a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicity. A further four chapters discuss sea severity, extreme sea state, the directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally the stochastic properties of non-Gaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitable as a text for graduate students of naval, ocean and coastal engineering. It will also serve as a useful reference for research scientists and engineers working in this field. |

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### Contents

1 Description of random seas | 1 |

2 Spectral analysis | 13 |

23 Wave spectral formulations | 33 |

24 Modification of wave spectrum for moving systems | 50 |

25 Higherorder spectral analysis | 52 |

3 Wave amplitude and height | 58 |

4 Wave height and associated period | 103 |

5 Sea severity | 123 |

75 Formulation of the wave energy spreading function | 216 |

8 Special wave events | 218 |

82 Group waves | 232 |

83 Freak waves | 252 |

9 NonGaussian waves waves in finite water depth | 255 |

Appendix A Fundamentals of probability theory | 283 |

Appendix B Fundamentals of stochastic process theory | 294 |

Appendix C Fourier transform and Hilbert transform | 300 |

6 Estimation of extreme wave height and sea state | 149 |

7 Directional characteristics of random seas | 175 |

74 Estimation of directional energy spreading from data | 196 |

304 | |

317 | |

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applying asymptotic breaking waves buoy comparison computed considered cumulative distribution function data obtained deﬁned deﬁnition denoted derived developed dimensionless equation estimated evaluated example extreme value extreme value distribution extreme wave height ﬁgure ﬁrst Fourier series ftmction func function of wave gamma gamma distribution Gaussian random process given in Eq half-cycle excursions Hence histogram hurricane joint probability density Longuet-Higgins marine systems measured data method modiﬁed narrow-band non-Gaussian normal distribution observed ocean waves Ochi positive maxima probability density function probable extreme random seas random variable random waves Rayleigh distribution relationship sample space sea severity shown in Figure signiﬁcant wave height speciﬁed level spectral density function spectral formulation statistical properties statistically independent stochastic process theoretical tion Type variance velocity wave breaking wave data wave displacement wave energy wave groups wave height data wave period wave proﬁle wave record wave spectrum Weibull distribution wind speed wind-generated